/pdf/handbook-of-magma-functions-5anhrdxxj3.pdf

Handbook of magma functions

1. (i) Suppose K is a conjugacy class of Sn contained in An; then K is called split if K is a union of two conjugacy classes of An. Show that the number of split conjugacy classes contained in An is equal to the number of characters χ ∈ Irr(Sn) such that χAn is not irreducible. (Hint. Consider the vector space of class functions on An which are invariant under conjugation by the transposition (12).)

/pdf/character-theory-of-finite-groups-mraeb8b123.pdf

Character Theory of Finite Groups

Journal of Algebra

Introduction Gradings on algebras Associative algebras Classical Lie algebras Composition algebras and type $G_2$ Jordan algebras and type $F_4$ Other simple Lie algebras in characteristic zero Lie algebras of Cartan type in prime characteristic Affine group schemes Irreducible root systems Bibliography Index of Notation Index

Gradings on Simple Lie Algebras

Algorithms and Programming

Cocyclic Hadamard Matrices and Hadamard Groups Are Equivalent

Combinatorial design theory is a source of simply stated, concrete, yet difficult discrete problems, with the Hadamard conjecture being a prime example. It has become clear that many of these problems are essentially algebraic in nature. This book provides a unified vision of the algebraic themes which have developed so far in design theory. These include the applications in design theory of matrix algebra, the automorphism group and its regular subgroups, the composition of smaller designs to make larger designs, and the connection between designs with regular group actions and solutions to group ring equations. Everything is explained at an elementary level in terms of orthogonality sets and pairwise combinatorial designs--new and simple combinatorial notions which cover many of the commonly studied designs. Particular attention is paid to how the main themes apply in the important new context of cocyclic development. Indeed, this book contains a comprehensive account of cocyclic Hadamard matrices. The book was written to inspire researchers, ranging from the expert to the beginning student, in algebra or design theory, to investigate the fundamental algebraic problems posed by combinatorial design theory.

http://www.maths.nuigalway.ie/%7Edane/surv-175-delauney-cov.pdf

Algebraic Design Theory

Cocyclic Hadamard matrices and difference sets

https://www.math.auckland.ac.nz/~obrien/research/jsc-Recognition.pdf

Recognizing finite matrix groups over infinite fields

http://www.maths.nuigalway.ie/%7Edane/Tits.pdf

Dane Flannery

Papers

Cocyclic Hadamard Matrices and Hadamard Groups Are Equivalent

Algebraic Design Theory

Cocyclic Hadamard matrices and difference sets

Recognizing finite matrix groups over infinite fields

Algorithms for the Tits alternative and related problems